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1972•Journal of Geophysical Research AtmospheresRequires access

A method for computing the gravitational attraction of three-dimensional bodies in a spherical or ellipsoidal Earth

Lane R. Johnson, Joe J. Litehiser

Open publisher page 26 citations

Abstract

A method is presented for calculating the gravitational attraction of three-dimensional bodies of arbitrary shape within a spherical or ellipsoidal earth. The sphericity of the earth is treated exactly by developing the formulas in a spherical coordinate system and the ellipticity is treated approximately by including only first-order terms in the flattening of the earth. The three-dimensional body is specified by giving its shape and density at a number of successive depths. The method is well suited for evaluation on a digital computer, and calculations are presented for a couple of examples that demonstrate in a quantitative manner the relative effects of sphericity and ellipticity.

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What this paper is about

A method is presented for calculating the gravitational attraction of three-dimensional bodies of arbitrary shape within a spherical or ellipsoidal earth. The sphericity of the earth is treated exactly by developing the formulas in a spherical coordinate system and the ellipticity is treated approximately by including only first-order terms in the flattening of the earth. The three-dimensional body is specified by giving its shape and density at a number of successive depths. The method is well suited for evaluation on a digital computer, and calculations are presented for a couple of examples that demonstrate in a quantitative manner the relative effects of sphericity and ellipticity.

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Available abstract

A method is presented for calculating the gravitational attraction of three-dimensional bodies of arbitrary shape within a spherical or ellipsoidal earth. The sphericity of the earth is treated exactly by developing the formulas in a spherical coordinate system and the ellipticity is treated approximately by including only first-order terms in the flattening of the earth. The three-dimensional body is specified by giving its shape and density at a number of successive depths. The method is well suited for evaluation on a digital computer, and calculations are presented for a couple of examples that demonstrate in a quantitative manner the relative effects of sphericity and ellipticity.

Key concepts: Flattening, Sphericity, Ellipsoid, Figure of the Earth, Physics, Spherical coordinate system, Gravitational field, Ellipsoidal coordinates

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